Details

Time bar (total: 2.0m)

sample139.0ms

Algorithm
intervals
Results
41.0ms265×body80nan
39.0ms143×body80valid
36.0ms113×body160valid

simplify459.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
458.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize45.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
0.8b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
21×sqrt-prod
19×pow1
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×insert-posit16 add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 179
Calls
4 calls:
Slowest
26.0ms
(* (/ Om Omc) (/ Om Omc))
20.0ms
(* (/ t l) (/ t l))
8.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series260.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
42.0ms
(* (/ t l) (/ t l))
31.0ms
(* (/ Om Omc) (/ Om Omc))
19.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify24.2s

Counts
243 → 191
Calls
243 calls:
Slowest
491.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
428.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
396.0ms
(* (* (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))) (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
387.0ms
(sqrt (- 1 (* 2 (* (/ t l) (/ t l)))))
348.0ms
(* (/ Om Omc) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))

prune3.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.0b

localize28.0ms

Local error

Found 4 expressions with local error:

7.3b
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
0.8b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
0.3b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
61×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×insert-posit16 add-log-exp
3×sqrt-prod
2×pow2 frac-times pow-plus sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square asin-acos sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 161
Calls
4 calls:
Slowest
32.0ms
(* (/ t l) (/ t l))
18.0ms
(* (/ Om Omc) (/ Om Omc))
4.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

series185.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
45.0ms
(* (/ Om Omc) (/ Om Omc))
40.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))

simplify16.8s

Counts
209 → 173
Calls
209 calls:
Slowest
510.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
480.0ms
(sqrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
466.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
395.0ms
(* (/ Om Omc) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
339.0ms
(* (/ t l) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))

prune2.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.0b

localize89.0ms

Local error

Found 4 expressions with local error:

14.5b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
14.5b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
14.5b
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
10.1b
(sqrt (/ (+ 1 (/ Om Omc)) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
16×sqrt-prod
11×add-sqr-sqrt *-un-lft-identity
9×cbrt-prod flip3-+ add-cube-cbrt flip-+
8×associate-/r/
5×pow1 times-frac
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3
2×rem-sqrt-square associate-*l/ associate-*r/
1×sqrt-pow1 pow1/2 sqrt-div div-inv distribute-lft-out
Counts
4 → 71
Calls
4 calls:
Slowest
34.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
13.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
4.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
4.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

series763.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
211.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
189.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
186.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))
176.0ms
(cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))

simplify19.9s

Counts
109 → 83
Calls
109 calls:
Slowest
635.0ms
(sqrt (/ (sqrt (+ 1 (/ Om Omc))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l)))))))
558.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))))))
507.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))
497.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (* (cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l)))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))
494.0ms
(cbrt (- (* 1 1) (* (* 2 (* (/ t l) (/ t l))) (* 2 (* (/ t l) (/ t l))))))

prune1.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.0b

localize52.0ms

Local error

Found 4 expressions with local error:

14.7b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
14.7b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
14.7b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
10.1b
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
45×times-frac
40×add-sqr-sqrt *-un-lft-identity
31×add-cube-cbrt
18×difference-of-squares
12×pow1
9×sqrt-pow1 pow1/3
7×cbrt-div
6×associate-/r/
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×flip3-+ sqrt-div flip-+ div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 associate-*l/ associate-*r/ sqrt-prod
Counts
4 → 116
Calls
4 calls:
Slowest
19.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
5.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
4.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
4.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
295.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))))
262.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
251.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))
250.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))

simplify37.8s

Counts
193 → 128
Calls
193 calls:
Slowest
680.0ms
(sqrt (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
379.0ms
(cbrt (/ (- 1 (/ Om Omc)) (+ 1 (* 2 (* (/ t l) (/ t l))))))
359.0ms
(* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l))))))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (+ 1 (* 2 (* (/ t l) (/ t l)))))))
345.0ms
(cbrt (- 1 (* 2 (* (/ t l) (/ t l)))))
343.0ms
(cbrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))) (cbrt (+ 1 (* 2 (* (/ t l) (/ t l))))))))

prune2.3s

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 4.0b

regimes658.0ms

Accuracy

98.5% (0.1b remaining)

Error of 5.8b against oracle of 5.7b and baseline of 10.5b

bsearch10.0ms

end0.0ms

sample5.1s

Algorithm
intervals
Results
2.0s3769×body160valid
1.6s7947×body80nan
969.0ms4231×body80valid